Download Adding and Subtracting Fractions

3
8
Adding and Subtracting
Fractions
By Graeme Henchel
http://hench-maths.wikispaces.com
Adding Fractions with common
denominators
3 4
7


8
8 8
Adding Fractions with different
denominators
Problem:
You can’t add fractions with different denominators
without getting them ready first. They will be ready to
add when they have common denominators
Solution:
Turn fractions into equivalent fractions with a
common denominator
that is find the Lowest
Common Multiple (LCM) of the two denominators
Finding the
Lowest Common Denominator
• The lowest common multiple of two numbers is
the lowest number in BOTH lists of multiples
1 1

2 3
Multiples of 2 are 2, 4, 6, 8, 10……
Multiples of 3 are 3, 6, 9, 12, ………
What is the lowest common
multiple?
Finding the
Lowest Common Denominator
• The lowest common multiple of two numbers is
the lowest number they will BOTH divide into
1 1

2 3
2 divides into 2, 4, 6, 8…..
3 divides into 3, 6, 9….
What is the lowest number 2 and 3
both divide into?
1 1

2 3
You can’t add fractions with
different denominators
+
The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths
1 3 1 2 3 2 5
     
2 3 3 2 6 6 6
Special form of 1
1
2

2
5
Lowest common denominator is 10 so make all fractions tenths
5 4 9
 
10 10 10
1
1

3
4
Turn both fractions into twelfths
4 3
7
 
12 12 12
?
?
3 3 2 7
2
9 14 23
   




1
3 7 3 7
21 21 21 21 21 21
It is 3/3
It is 7/7
So I multiply
So I multiply
3/7 by 3/3
2/3 by 7/7
Finally the fractions are READY to
add. I just have to add the
numerators
9+14=23
What
is special
the
lowest
What
What
special
form
formnumber
3 and
77divide
ofBOTH
1 of
will1 change
will
change
3 into?
to 21.
to 21.
Hmmmm?
Hmmmm?
It is 21.
So
that is my
Hmmmmm??????
common denominator
Now 3x3=9 and 2x7=14
Now I know the new
numerators
Adding Mixed Numbers
• Separate the fraction and the whole number sections,
add them separately and recombine at the end
22
11
22

 55
11
33



7

5
6
7

5
6
